Measure-valued solutions for the equations of polyconvex adiabatic thermoelasticity
Analysis of PDEs
2018-08-28 v1
Abstract
For the system of polyconvex adiabatic thermoelasticity, we define a notion of dissipative measure-valued solution, which can be considered as the limit of a viscosity approximation. We embed the system into a symmetrizable hyperbolic one in order to derive the relative entropy. However, we base our analysis in the original variables, instead of the symmetric ones (in which the entropy is convex) and we prove measure- valued weak versus strong uniqueness using the averaged relative entropy inequality.
Keywords
Cite
@article{arxiv.1808.08382,
title = {Measure-valued solutions for the equations of polyconvex adiabatic thermoelasticity},
author = {Cleopatra Christoforou and Myrto Galanopoulou and Athanasios E. Tzavaras},
journal= {arXiv preprint arXiv:1808.08382},
year = {2018}
}